Coexistence of Localized and Extended States in Disordered Systems

Abstract

It is commonly believed that Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a band in a class of disordered quasi-1D and quasi-2D systems. The systems are partially disordered in a way that a band of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The extended states can overlap with the localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multi-chain and multi-layer systems.

5 pages, 3 figures

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• Topological linelike bound states in the continuum
• Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system
• Localization of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Robust Topological Bound States in the Continuum in a Quantum Hall Bar with an Anti-dot